This preview shows pages 1–5. Sign up to view the full content.
1
1
1.
Diversification
A stock market speculator is considering two investment
opportunities
x
An investment in the first company would yield an
income of 50,000 in a strong economy and an income of
10,000 in a recession.
x
The second company is much more recession proof and
yield 30,000 in a strong economy, but 20,000 in a
recession.
x
The investor believes that the chances of a strong
economy are 50/50.
x
The investor's utility function is U(Y)=ln Y, where Y is the
investor's income from his investment.
2
1.
Diversification continued
a) Suppose that he must choose one company or the other.
Which investment has the greater expected yield?
Which
investment has the greater expected utility for the
speculator?
x
For firm 1, EU=.5 ln 50000 +.5 ln 10000 = 10.015,
EV=.5*50000+.5*10000=30000.
x
For firm 2, EU=.5 ln 30000 +. 5ln 20000 = 10.106,
EV=.5*30000+.5*20000=25000
x
Firm 1 is better in expected value terms, but firm 2 is
better in expected utility terms, since the individual is
risk averse.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 2
3
1.
Diversification continued
b) Without a forecaster, suppose that the speculator
can diversify and spread his funds equally
between the two firms.
Will he choose to invest
in both firms?
EU=.5 ln 40000 +.5 ln 15000 = 10.106, so he is
pretty much indifferent between a 50/50 split
and buying only firm 2.
4
1.
Diversification continued
c) What mix of firm 1 and firm 2 would maximize
expected utility to the speculator?
x
EU=.5 ln (
α
50000 + (1
α
)30000)
+.5 ln (
α
10000 + (1
α
)20000)
x
∂
EU/
∂α
=10000/(20000
α
+30000)
 5000/(10000
α
+20000)
x
α
=.25, so he will invest 25 percent in firm1 and
75 percent in firm 2
3
5
2.
Risk Aversion
x
Luke is a miner living in a poor third world country.
After
20 years of prospecting, he gets lucky and discovers $3
million in gold (his only wealth in the world).
He wants to
get the gold to the capital city, so he can retire and live off
his wealth.
x
Over the years, Luke has discovered that local bandits steal
his money on every other trip to the capital.
x
Luke considers two strategies:
Strategy A:
He makes one trip and takes all the money.
Strategy B:
He makes two trips and carries $1.5 million on
each trip.
6
2.
Risk Aversion Continued
a)
Show which strategy Luke should pick if U=W
.5
?
He is risk adverse.
Under strategy B, EU=.25 U(3)+.5
U(1.5)+.25 U(0)=1.045.
Under strategy A, EU=0.87.
He is better off with strategy B.
b)
Show which strategy Luke should pick if U=W
2
?
Now he is a risk preferrer.
Under strategy A, EU=4.5.
Under strategy B, EU=25 U(3)+.5 U(1.5)+.25
U(0)=3.375.
He is better off with strategy A.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 4
7
2.
Risk Aversion Continued
c)
Discuss how the characteristics of Luke's utility
functions in part a and b affect his choice between
strategies
.
The choice depends on risk aversion.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/08/2008 for the course ECON 101 taught by Professor Buddin during the Spring '08 term at UCLA.
 Spring '08
 Buddin

Click to edit the document details